The system shown in the schematic represents a model two-story building: Take m = 1 104 kg, m = 3 104 kg, k = 4 105 N/m, k = 2 105 N/m a) Derive the equations of motion of the system and represent them in a matrix form b) Find the natural frequencies of the system. c) Find the amplitude ratio of x2 vibration to x for all possible modes of vibration. d) What is the number of possible modes of vibrations. X2 X1 m2 K2 m k